On multiplication theorems for magic squares
In this paper, we present, prove, and illustrate a Composition Theorem for Magic Squares.Let M and N be magic squares of orders p and q, respectively. For k = 1,2..., q2, letMk = M + (k - 1) p2 Jpwhere Jp = p x p matrix of all 1's. Form the array Nm of order pq obtained by replacing each entry...
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1995
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oai:animorepository.dlsu.edu.ph:etd_bachelors-167532022-02-04T08:04:26Z On multiplication theorems for magic squares Antonio, Rosemarie M. Caleon, Heidee D.J. In this paper, we present, prove, and illustrate a Composition Theorem for Magic Squares.Let M and N be magic squares of orders p and q, respectively. For k = 1,2..., q2, letMk = M + (k - 1) p2 Jpwhere Jp = p x p matrix of all 1's. Form the array Nm of order pq obtained by replacing each entry of N by Mk. Then Nm is a magic square of order pq.Using this composition theorem, we can compose the approximate magic square N = 14 32 with anu p x p matrix M to form a magic square of order 2p. 1995-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/16240 Bachelor's Theses English Animo Repository Magic squares Mathematical recreations Matrices Number theory |
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Magic squares Mathematical recreations Matrices Number theory |
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Magic squares Mathematical recreations Matrices Number theory Antonio, Rosemarie M. Caleon, Heidee D.J. On multiplication theorems for magic squares |
| description |
In this paper, we present, prove, and illustrate a Composition Theorem for Magic Squares.Let M and N be magic squares of orders p and q, respectively. For k = 1,2..., q2, letMk = M + (k - 1) p2 Jpwhere Jp = p x p matrix of all 1's. Form the array Nm of order pq obtained by replacing each entry of N by Mk. Then Nm is a magic square of order pq.Using this composition theorem, we can compose the approximate magic square N = 14 32 with anu p x p matrix M to form a magic square of order 2p. |
| format |
text |
| author |
Antonio, Rosemarie M. Caleon, Heidee D.J. |
| author_facet |
Antonio, Rosemarie M. Caleon, Heidee D.J. |
| author_sort |
Antonio, Rosemarie M. |
| title |
On multiplication theorems for magic squares |
| title_short |
On multiplication theorems for magic squares |
| title_full |
On multiplication theorems for magic squares |
| title_fullStr |
On multiplication theorems for magic squares |
| title_full_unstemmed |
On multiplication theorems for magic squares |
| title_sort |
on multiplication theorems for magic squares |
| publisher |
Animo Repository |
| publishDate |
1995 |
| url |
https://animorepository.dlsu.edu.ph/etd_bachelors/16240 |
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1772835041613709312 |